Adaptive feed forward-feedback control of the concentration of a selected ion of a solution

ABSTRACT

A control system for controlling the flow of reagent into a reactor for the correction of the concentration of a selected ion in the influent to the reactor so as to provide a desired concentration in the effluent stream from the reactor. A feedback controller having proportional and reset responses is provided to control the flow of reagent to maintain the logarithm of the concentration of the ion in the effluent at its set point. The control signal from the feedback controller is multiplied by a feedforward control signal responsive to changes in the logarithm of the ion concentration of the influent, the effluent set point, and influent flow. The resulting product is then summed with the feedforward control signal to provide the final control signal required to control a linear operator for modification of the reagent flow to maintain the logarithm of the ion concentration in the effluent at the set point.

United States Patent [191 Friedmann -et a1.

[52] US. Cl. 23/230 A, 23/253 A [51] Int. Cl. G05b 13/02, G05d 21/02[58] Field of Search 23/253 A, 230 A [56] References Cited UNITED STATESPATENTS 3,656,911 4/1972 Hobbs 23/253 A FOREIGN PATENTS OR APPLICATIONS559,001 1/1944 Great Britain 23/253 A 638,073 5/1950 Great Britain23/253 A OTHER PUBLICATIONS Shinskey, F. 0., Process ControlMcGraw-Hill; 1967, pp. 280-281. Shinskey, F. G., Feedforward Control ofpH, Instrumentation Technology, June, 1968, pp. 65-69. Shinskey et al.,Adaptive Feedback Applied to Feed- Systems,

FEEDFORWARD CONTROLLER 38 Eli FA 11] 3,791,793 [451 Feb. 12, 1974forward pH Control," 1970 Phila. ISA Confi, Preprint pp. 565-570.

Williams, .1. J. et al., Progress in Direct Digital Control, ISA, 1959,page 203.

Wilson H. S. et 211., ISA Preprint l 1.l-264, 10/12/64.

Primary Examiner-Barry S. Richman Attorney, Agent, or Firm-William G.Miller, Jr.; Raymond F. MacKay [5 7] ABSTRACT A control system forcontrolling the flow of reagent into a reactor for the correction of theconcentration of a selected ion in the influent to the reactor so as toprovide a desired concentration in the effluent stream from the reactor.A feedback controller having proportional and reset responses isprovided to control the flow of reagentto maintain the logarithm of theconcentration of the ion in the effluent at its set point. The controlsignal from the feedback controller is multiplied by a feedforwardcontrol signal responsive to changes in the logarithm of the ionconcentration of the influent, the effluent set point, and influentflow. The resulting product is then summed with the feedforward controlsignal to provide the final control signal required to control a linearoperator for modification of the reagent flow to maintain the logarithmof the ion concentration in the effluent at the set point.

11 Claims, 3 Drawing Figures 22 W'EEDBAcK CONTROLLER PM'ENIEB FEB I 2I974 SHEET 1 0F 2 PXC 2 4 AE A IR 2 m. WM F 2 CL L, 0 mF fin FR M DRW DA ET EM x a.. m FC P C v I n/O 3 1 6 1\ 2 X m A m FIG. 2

PATENIEDIEM 21914 sum 2 or 2 FIG.

ADAPTIVE FEEI) FORWARD-FEEDBACK CONTROL OF THE CONCENTRATION OF ASELECTED ION OF A SOLUTION BACKGROUND OF THE INVENTION Conventionally,systems for controlling the concentration of a selected ion of asolution, such as pH control systems, have used simple feedback controlin which the pH of the effluent from a reactor is compared to a setpoint and a control signal which may include both proportional andintegral response is fed back to a valve which controls the flow ofreagent to the reactor. In many pH control systems, for example,disturbances'in the flow of influent to the reactor or the compositionof the influent stream as well as variations in the strength of thereagent and changes which may occur in the buffering capacity of theinfluent must be taken into account in the control of the reagent flowin order to accomplish suitable control of the effluent. In order toprovide modification of the normal feedback control to take into accountsuch disturbances, the addition of feedforward control has beenattempted by others in the past. The systems which have been provided toincorporate both feedforward and feedback control usually provided onlyfor a summation of the feedforward and feedback control signals and theresulting control did not suitably adapt to changes in reagent strengthor changes in the buffering capacity of the influent, for example. Somesystems have been di rected solely to the operation of equal percentagevalves for the control of the reagent strength and have not been usefulto control linear operators in which the reagent is modified by a valveor metering pump as a linear function of the control signal to which theoperator is responding.

It is, therefore, an object of this invention to provide an improvedfeedforward-feedback control of the negative logarithm of theconcentration, pX, of a selected ion, X, of a solution.

A further object of this invention is the provision of an adaptivefeedforward-feedback control of pH which will manipulate a linearoperator in a manner which will suitably adapt for changes in reagentstrength as wellas changes in'the buffering capacity of the influentstream.

SUMMARY OF THE INVENTION The present invention provides a method forcontrolling to a set point the logarithm of the concentration of aselected ion in the effluent from a reactor process in which thelogarithm of the concentration of that-ion in the influent is modifiedby the addition ofa reagent and the flow of the reagent is a linearfunction of the magnitude of a final control signal. This methodcomprises the steps of producing in response to the logarithm of the ionconcentration in the influent a feedforward control signal indicative ofthe reagent flow required to maintain the logarithm of the ionconcentration in the effluent at its set point under certain processconditions and the producing of a final control signal for modifying thereagent flow as a function of the product of the feedforward controlsignal and a function of the deviation of the logarithm of the ionconcentration in the ef fluent from its set point. The invention alsoprovides means for carrying out the above mentioned steps.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. I is a diagram of a system forcontrolling the logarithm of the concentration ofa specific ion ofasolution in which the control elements are shown in block diagram form.

FIG. 2 is a functional diagram of one form which the feedforwardcontroller may take.

FIG. 3 is a graphic representation of the titration DESCRIPTION OF THEPREFERRED EMBODIMENT For the purposes of this description and the claimspX will be used to indicate the negative logarithm of the concentrationor activity of a selected ion, X, which is measured by an electrodesystem which generates a Nernstian response. For example, if theselected ion is the hydrogen ion, pX becomes the well known quantity pH.X can, of course, be any ofa number of other ions such as chloride, forexample. All reference to the logarithm of the concentration is intendedto refer to the negative logarithm of the concentration where polarityis of significance since, for example, pH is equal to the negativelogarithm of the hydrogen ion concentration.

In FIG. 1 a continuous stirred-tank reactor is used for pX control. Thetank 10, which is continuously stirred by the motor operated stirrer 12provides the necessary retention time and mixing to provide for acontrol of the K of the liquid introduced by way of the influent streamA flowing through pipe 14. The control is accomplished by modifying theflow of the reagent B into the reactor by way of the pipe 16 so that theeffluent which is carried away from the reactor by way of pipe 18 formsan effluent stream C whose pX is maintained at a predetermined setpoint. I

A feedback controller 20 providing both proportional and integral(reset) response produces a feedback signal S on its output line 22 as aproportional and integral function of the difference between the pH ofthe effluent stream, as measured by the pH measuring element 24, and thepH set point, as established by the adjustment of knob 26A on the signalsource 26. Thus, the controller 20 responds to a signal on line 28indicative of the pX of the effluent, pX and the signal on line 30 fromthe signal source 26 indicative of the set point, pX representing thedesired pX of the effluent.

The feedback control is preferably of the type which provides a zerooutput signal S whenever the effluent pX is at its set point; namely,when the signal on line 28 agrees with the signal on line 30, assumingno integral response has been accumulated. Thus, the input from line 22to the feedforward controller 34 will be zero unless the pX of theeffluent deviates from the set point.

The feedforward controller 34 is responsive to the pX of the influentstream, pX by virtue of the input on line 36 from the pX measuringelement 38, which is arranged to detect the pX of the influent. Thecontroller 34 likewise responds to changes in the flow of influent inpipe 14 by virtue of the input signal on line 40 from the flow measuringdevice 42 which responds to the pressure differential across orifice 44.

The feedforward controller is also shown as being responsive to a signalon line 48 which is representative of the set point for the pX of theeffluent and may, as shown in FIG. 1, be derived by connection throughline 30 to signal source 26 which provides the set point signal, pX

The manner in which the feedforward controller 34 responds to its inputsignals will be further explained in connection with the description ofFIG. 2. However, as shown in FIG. 1, the feedforward controller 34produces a final control signal, F on line 50 which causes theelectro-pneumatic converter 52 to provide on line 54 a correspondingpneumatic signal to the diaphragm operated valve 56, which is preferablya valve which adjusts the flow of reagent through pipe 16 as a linearfunction of the magnitude of the pneumatic signal on line 54.

In FIG. 2, there is shown a functional block diagram of one form whichthe feedforward controller 34 of FIG. 1 may take. In FIG. 2 there isprovided a means for producing on line 60, a feedforward control'signalwhich is responsive to the pX of the influent stream, pX and to themagnitude of the flow of the influent, F,,, as well as the pX set pointfor the effluent, pX

As shown in FIG. 2, the feedforward control signal on line 60 ismultiplied by the feedback control signal on line 62 by multiplier 64with the product of that multiplication appearing on line 66 as an inputto the summer 68. The summer 68 operates to sum the signal on line 66with the feedforward control signal on line 60 so that the resulting sumis a'signal F namely, the final control signal. Desirably, F varieslinearly with the required magnitude of reagent flow needed to correctthe pX of the influent to produce the desired pX in the effluent.

As shown in FIG. 2, the feedback control signal appearing on line 62 isobtained by multiplying the feedback signal S from the feedbackcontroller by a gain factor K introduced by unit 70, which may be apotentiometer, so that the signal supplied on line 62 is representativeof. K S.

It will be evident from FIG. 2 that the signal on line 50 is formed fromthe sum of the feedforward control signal and the product of thefeedforward and feedback control signals. The feedforward control signalon line 60 is produced in accordance with the algorithm I(,F, (R Rwhere: i

F,, flow of reagent, vol./time R, vol. reagent/vol. influent, ateffluent pH set point according to titration curve of influent at pX(FIG. 3)

R, vol. reagent/vol. influent, at influent pX according to titrationcurve. (FIG. 3)

K feedforward gain.

For titration of a strong acid by a strong base, when X is the hydrogenion, the following approximation is valid.

pH, pH of the influent.

pH, pH set point of effluent.

pH pH of reagent.

Referring to the titration curve of FIG. 3, there is illustrated therelationship between the terms R and R,,. It will also be evident fromFIG. 3 that the area of the titration curve which is significant isessentially exponential in shape. Thus, the function generator 72provides an output signal on line 74 which is exponentially related tothe input signal on line 36 representative of the measured pX in theinfluent stream. Similarly, the function generator 78 provides on line80 a signal which is exponentially related to the signal on line 48representative of the pX set point, pX

The summer 82 operates to sum the signals from lines 80 and 74. Sincethe signal on line 74 is of a sign opposite that on line 80, the outputon line 84 is representative of the quantity (R R That signal is thenmultiplied by a gain factor K, which may be provided by unit 86, whichmay be a potentiometer, so that the input to the multiplier 88 from theunit 86 is representative of the quantity K,(R R The other input to themultiplier 88 is from line 40 and is representative of the mea suredflow in the influent pipe 14. Thus, there is produced on the output line60 of multiplier 88 the feedforward control signal representing thequantity K1FA(RSRA)- The previously explained multiplication of thefeedforward control signal and feedback control signal by multiplier 64and the summation 'of that product with the feedforward control signalproduces a final control signal on line 50 which represents thealgorithm Kif t isi dtli 132; J I

By providing a final control signal which is a function of the productof the feedforward control signal and the feedback control signal, thefeedforward control signal is adapted by the feedback control signal soas to provide a control which will correct the reagent flow to correctfor changes in the strength of the reagent to changes in the bufferingcapacity of the influent as well as other changes which would have theeffect of changing the titration curve of FIG. 3. This adaptation of thefeedforward controller will cause that controller to properly adjust thereagent flow subsequent to those disturbances.

Viewing the control system in another way, it may be considered that theconventional feedforwardfeedback control of the reagent flow which wouldinvolve the summation of the feedforward and feedback control signalshas been modified by making the feedback control signal adaptive sincethe feedback control signal is, as shown in FIG. 2, multiplied by thefeedforward control signal before the summation is carried out.

Using the pH control system described above may, under certain systemconditions, allow for the simplification of the feedforward controller.For example, in many applications, such as waste neutralization, theeffluent set point remains fixed and it would, therefore, be unnecessaryto provide the signal R on line 80. Instead, the gain K, could bealtered to account for the absence of that signal. Similarly, the flowof influent may not vary over a range sufficient to significantly modifythe operation of the feedforward control and hence the signal F,, online 40 could be omitted. In that situation any flow changes would becompensated for by the feedback control. Thus, under some situations thefeedforward controller may be responsive to-a single variable; namely,pX,,.

Those skilled in the art will recognize that the feedback controller maybe any of a number of commercially available controllers which provideboth proportional and reset responses. Similarly, the feedforwardcontroller may take any of a number of forms. it may, for example, be acurrent adjusting type which produces an output signal which is acurrent of varying magnitude. Thus, F may be presented to the converter52 as a current which the converter must convert to a correspondingpneumatic signal for operation of the valve operator.

The functions shown in the block diagram of FIG. 2, are usually mosteasily carried out with voltage signals, thus, it may be necessary toconvert the resulting signal F to a current signal. Such requirementsare related to the details of the design of the control system and arewell known in the art.

We claim:

1. The method for controlling to a set point, the pX of the effluentfrom a reaction process in which the pX of the influent is modified bythe addition of a reagent and the flow of the reagent is a linearfunction of the magnitude of a final control signal comprising the stepsof:

producing in response to the pX of the influent a feedforward controlsignal indicative of the reagent flow required to maintain the pX of theeffluent at its set point under certain process conditions, and

producing a final control signal for modifying the reagent flow as afunction of the weighted sum of said feedforward control signal and theproduct of said feedforward control signal and a function of thedeviation of the pX of the effluent from said set point.

2. The method as set forth in claim 1 in which the step of producing thefeedforward control signal is responsive to the pX of the influent andthe magnitude of the influent flow to the reactor.

3. The method as set forth in claim 1 in which the step of producing afeedforward control signal is responsive to the pX of the influent, themagnitude of the influent flow to the reactor, and said set point.

4. The method as set forth in claim 1 in which the function of thedeviation of the pX of the effluent from said set point includesproportional and reset responses to the deviation of the pX of theeffluent from its set point.

5. The method for controlling to a set point, the pX of the effluentfroma reactor process in which the pX of the influent is modified by theaddition of a reagent and the flow of the reagent is a linear functionof the magnitude of a final control'signal comprising the steps of,

producing in response to the pX of the influent, the

magnitude of the influent flow, and the set point, a feedforward controlsignal indicative of the reagent flow required to change the pX of theinfluent toward the set point,

producing a feedback control signal in accordance with the deviation ofthe pX of the effluent from said set point, and

producing a final control signal for modifying the flow of said reagentas a function of the sum of said feedforward control signal and theproduct of said feedforward and feedback control signals.

6. A system for controlling the pX of the effluent from a processreactor at a predetermined set point by linearly varying the reagentflow to the reactor in response to a final control signal comprising:

means responsive to the pX of the influent for producing a feedforwardcontrol signal indicative of the reagent flow required to change the pXof the influent to the set point under certain process conditions, and

means for producing said final control signal as a function of theweighted sum of said feedforward control signal and the product of saidfeedforward control signal and a function of the deviation of the pX ofthe effluent from said set point.

7. A system as set forth in claim 6 in which the means for producing thefeedforward control signal is responsive to the pX of the influent andthe magnitude of the influent flow to the reactor.

8. A system as set forth in claim 6 in which the means for producing thefeedforward control signal is responsive to the pX of the influent, themagnitude of the influent flow to the reactor and said set point.

9. A system for controlling the pX of the effluent from a processreactor at a predetermined set point by linearly varying the reagentflow to the reactor in response to a final control signal comprising,

means for producing a feedforward control signal in response to the pXof the influent,

means for producing a feedback control signal in proportion to thedeviation of the pX of the effluent from its set point and the integralof said deviation, and

means for summing said feedforward control signal with the product ofsaid feedforward control signal and said feedback control signal toproduce said final control signal.

10. A system for controlling the pX of the effluent from a processreactor at a predetermined set point by linearly varying the reagentflow to the reactor in response to a final control signal comprising:

means for producing a feedforward control signal in response to themagnitude of the influent flow to the reactor, the pX of the influent,and said set point,

means for producing a feedback control signal in accordance with thedeviation of the pX of the effluent from said set point, and means forcombining said feedforward control signal and said feedback controlsignal to produce said final control signal as a function of the productof said feedforward control signal and said feedback control signal,said function of the product of said feedforward control signal and saidfeedback control signal including the sum of the feedforward controlsignal and the product of the feedforward control signal and thefeedback control signal.

11. A system as set forth in claim 10 in which the means for producing afeedback control signal has both proportional and reset response to thedeviation of the pX of the effluent from its set point.

2. The method as set forth in claim 1 in which the step of producing thefeedforward control signal is responsive to the pX of the influent andthe magnitude of the influent flow to the reactor.
 3. The method as setforth in claim 1 in which the step of producing a feedforward controlsignal is responsive to the pX of the influent, the magnitude of theinfluent flow to the reactor, and said set point.
 4. The method as setforth in claim 1 in which the function of the deviation of the pX of theeffluent from said set point includes proportional and reset responsesto the deviation of the pX of the effluent from its set point.
 5. Themethod for controlling to a set point, the pX of the effluent from areactor process in which the pX of the influent is modified by theaddition of a reagent and the flow of the reagent is a linear functionof the magnitude of a final control signal comprising the steps of,producing in response to the pX of the influent, the magnitude of theinfluent flow, and the set point, a feedforward control signalindicative of the reagent flow required to change the pX of the influenttoward the set point, producing a feedback control signal in accordancewith the deviation of the pX of the effluent from said set point, andproducing a final control signal for modifying the flow of said reagentas a function of the sum of said feedforward control signal and theproduct of said feedforward and feedback control signals.
 6. A systemfor controlling the pX of the effluent from a process reactor at apredetermined set point by linearly varying the reagent flow to thereactor in response to a final control signal comprising: meansresponsive to the pX of the influent for producing a feedforward controlsignal indicative of the reagent flow required to change the pX of theinfluent to the set point under certain process conditions, and meansfor producing said final control signal as a function of the weightedsum of said feedforward control signal and the product of saidfeedforward control signal and a function of the deviation of the pX ofthe effluent from said set point.
 7. A system as set forth in claim 6 inwhich the means for producing the feedforward control signal isresponsive to the pX of the influent and the magnitude of the influentflow to the reactor.
 8. A system as set forth in claim 6 in which themeans for producing the feedforward control signal is responsive to thepX of the influent, the magnitude of the influent flow to the reactorand said set point.
 9. A system for controlling the pX of the effluentfrom a process reactor at a predetermined set point by linearly varyingthe reagent flow to the reactor in response to a final control signalcomprising, means for producing a feedforward control signal in responseto the pX of the influent, means for producing a feedback control signalin proportion to the deviation of tHe pX of the effluent from its setpoint and the integral of said deviation, and means for summing saidfeedforward control signal with the product of said feedforward controlsignal and said feedback control signal to produce said final controlsignal.
 10. A system for controlling the pX of the effluent from aprocess reactor at a predetermined set point by linearly varying thereagent flow to the reactor in response to a final control signalcomprising: means for producing a feedforward control signal in responseto the magnitude of the influent flow to the reactor, the pX of theinfluent, and said set point, means for producing a feedback controlsignal in accordance with the deviation of the pX of the effluent fromsaid set point, and means for combining said feedforward control signaland said feedback control signal to produce said final control signal asa function of the product of said feedforward control signal and saidfeedback control signal, said function of the product of saidfeedforward control signal and said feedback control signal includingthe sum of the feedforward control signal and the product of thefeedforward control signal and the feedback control signal.
 11. A systemas set forth in claim 10 in which the means for producing a feedbackcontrol signal has both proportional and reset response to the deviationof the pX of the effluent from its set point.